Flashcard 4 - Next Generation Advanced Algebra and Functions Flashcard Set for the ACCUPLACER Test

• Factoring greatest common factor (GCF) (example):
  \(x^4 + x^3 + x^2 = 0\) becomes \(x^2(x^2 + x + 1) = 0\)

• Quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

• Difference of squares: \(x^2 - y^2\) factors to \((x + y)(x - y)\)

• Completing the square: \(x^2 + bx = c\),
  add \(\frac{b}{2}^2\) to both sides,
  left side becomes \((x + \frac{b}{2})^2 = c + \frac{b}{2}\)

• Difference of cubes: \(x^3 - y^3 = (x - y)(x^2 + xy + y^2)\)

• Sum of cubes: \(x^3 + y^3 = (x + y)(x^2 - xy + y^2)\)

• Factor by grouping (example):
  \(x^3 + x^2 + x + 1 = 0\),
  group terms \((x^3 + x^2) + (x + 1) = 0\),
  factor from groups: \(x^2(x + 1) + 1(x + 1) = 0\),
  factor common expression: \((x + 1)(x^2 + 1) = 0\)

Mastery of the various factoring methods reduces the complexity of many problems and enables the critical points and information for various functions to be readily found. Such information can then be used to produce graphical representations of seemingly complex functions. Factoring is a crucial skill that takes practice to develop.